In putting together this issue of CiSE, we knew three things: it would be difficult to list just 10 algorithms; it would be fun to assemble the authors and read their papers; and, whatever we came up with in the end, it would be controversial. We tried to assemble the 10 algorithms with the greatest influence on the development and practice of science and engineering in the 20th century. Following is our list (in chronological order): Metropolis Algorithm for Monte Carlo Simplex Method for Linear Programming Krylov Subspace Iteration Methods The Decompositional Approach to Matrix Computations The Fortran Optimizing Compiler QR Algorithm for Computing Eigenvalues Quicksort Algorithm for Sorting Fast Fourier Transform Integer Relation Detection Fast Multipole Method